The slope and y -intercept of the line $y = m x + b$ that best fits the three noncollinear points $( 2,2 ) , ( 3,3 )$ and $( 5,4 )$ are given by the solution of the following system of linear equations. $\left\{ \begin{array} { c }
77 m + 12 b = 46 \
12 m + 5 b = 8
\end{array} \right.$ Solve the system and find the equation of the best-fitting line. Round parameters to the nearest thousandth.
A) $y = 0.415 x + 1.188$
B) $y = 0.412 x - 1.188$
C) $y = 0.417 x + 1.188$
D) $y = 0.556 x + 0.266$
E) $y = 0.42 x + 1.188$

Question

The slope and y -intercept of the line $y = m x + b$ that best fits the three noncollinear points $( 2,2 ) , ( 3,3 )$ and $( 5,4 )$ are given by the solution of the following system of linear equations. $\left\{ \begin{array} { c } 
77 m + 12 b = 46 \
12 m + 5 b = 8
\end{array} \right.$ Solve the system and find the equation of the best-fitting line. Round parameters to the nearest thousandth.
A) $y = 0.415 x + 1.188$
B) $y = 0.412 x - 1.188$
C) $y = 0.417 x + 1.188$
D) $y = 0.556 x + 0.266$
E) $y = 0.42 x + 1.188$

Quizplus · Accepted Answer

Solving the system of equations using methods like substitution or elimination gives $m \approx 0.556$ and $b \approx 0.266$. Thus, the equation of the best-fitting line is $y = 0.556x + 0.266$.

The Slope and Y -Intercept of the Line y=mx+by = m x + by=mx+b

The Slope and Y -Intercept of the Line $y = m x + b$